Lines n and p lie on the xy plane. Is the slope of line n less than slope of line p
(1) Lines n and p intersect at (5, 1)
(2) The y-intercept of line n is greater than the y intercept of p
Now let's consider statement 2, that says that the y intercept of n is greater than that of the y intercept of p. The slopes could be unequal (think about intersecting lines), or we could have parallel lines, in which case the slopes are equal. So, statement 2 is not sufficient on its own.
Now let's consider the statements together. The lines intersect at (5,1), and n has the higher y intercept. Let's look at 3 cases:
1) Both have y intercepts above y=1
Since n intersects higher, then we know n had further to descend, so its slope is steeper (but more negative) than p's. Thus, p has a greater slope.
2) n has intercept above y=1, p has intercept below
n would have a negative slope and p a positive, so p has a greater slope
3) Both have y intercepts below y=1
Both have positive slopes, but p has further to ascend. Thus, p has a greater slope.
Since combining the information tells us that p always has a greater slope, we have sufficient information with both statements and the answer is C, NOT B.
can you please help me understand these three cases. i am facing very difficulty with coordinate planes.
in case 1) how do we know that since n's slope is steeper it is more negative than p
thank you.
which is the best source for coordinate planes. i coudn't find any like this in MANHATTAN BOOKS
(1) Lines n and p intersect at (5, 1)
(2) The y-intercept of line n is greater than the y intercept of p
Now let's consider statement 2, that says that the y intercept of n is greater than that of the y intercept of p. The slopes could be unequal (think about intersecting lines), or we could have parallel lines, in which case the slopes are equal. So, statement 2 is not sufficient on its own.
Now let's consider the statements together. The lines intersect at (5,1), and n has the higher y intercept. Let's look at 3 cases:
1) Both have y intercepts above y=1
Since n intersects higher, then we know n had further to descend, so its slope is steeper (but more negative) than p's. Thus, p has a greater slope.
2) n has intercept above y=1, p has intercept below
n would have a negative slope and p a positive, so p has a greater slope
3) Both have y intercepts below y=1
Both have positive slopes, but p has further to ascend. Thus, p has a greater slope.
Since combining the information tells us that p always has a greater slope, we have sufficient information with both statements and the answer is C, NOT B.
can you please help me understand these three cases. i am facing very difficulty with coordinate planes.
in case 1) how do we know that since n's slope is steeper it is more negative than p
thank you.
which is the best source for coordinate planes. i coudn't find any like this in MANHATTAN BOOKS
